AMM: Automated Market Maker for pod tokens #193

Summary

Add a constant-product AMM (Uniswap v2 style) for trading sats ↔ pod tokens. The pod acts as the pool custodian — no smart contracts needed. Every swap advances the MRC20 trail on Bitcoin.

Why

The current .buy endpoint sells tokens at a fixed rate (--pay-rate). An AMM enables dynamic price discovery based on supply and demand. Combined with multi-token support (#192), this creates a full DEX inside a Solid pod.

Design

Endpoint: POST /pay/.amm

// Swap sats for tokens
{ "action": "swap", "sell": "sat", "amount": 100 }

// Swap tokens for sats
{ "action": "swap", "sell": "PODS", "amount": 10 }

// Add liquidity
{ "action": "add-liquidity", "sats": 1000, "tokens": 100 }

// Remove liquidity
{ "action": "remove-liquidity", "shares": 50 }

// GET /pay/.amm → pool state
{ "reserveSats": 10000, "reserveTokens": 1000, "k": 10000000, "price": 10, "fee": "0.3%", "lpShares": {...} }

Pricing formula

cost = (reserveSats * amount) / (reserveTokens - amount)  // + 0.3% fee to LPs

What already exists

• MRC20 token trails with transferToken({ from, to, amount }) — user-to-user transfers
• Webledger for sat balance tracking
• Pod escrow pattern (secondary market .sell/.swap already does this)
• NIP-98 auth on all endpoints

Components (~150 LOC)

Agent use case

An AI agent can read the pool state (GET /pay/.amm), calculate optimal trade size, and execute — no wallet UI needed. Multi-pod arbitrage becomes possible: if PODS trades at different prices on two pods, agents arb via withdraw/deposit.

UI

A Solid pane (see #184) could visualize the pool: price curve, depth, slippage calculator, LP positions. The server handles atomicity; the pane handles presentation.

Cross-chain AMM: testnet3 ↔ testnet4

The AMM doesn't have to be sats ↔ tokens. It can pool two different chains' coins — making the pod a cross-chain DEX.

Scenario: t3sat ↔ t4sat

Both Bitcoin testnet3 and testnet4 are running. Users deposit UTXOs from either chain. The pod tracks separate balances and the AMM prices one against the other.

Deposit testnet3 UTXO  →  credited as t3sat
Deposit testnet4 UTXO  →  credited as t4sat

Pool: 1000 t3sat × 5000 t4sat = k
Price: 1 t3sat = 5 t4sat

Swap 100 t3sat → receive ~454 t4sat (constant product)

Why this is a great first test

• Both are free coins — zero risk
• Tests multi-chain deposits, AMM, and per-chain balances together
• Creates real price discovery between two testnet economies
• Any agent with a faucet UTXO can participate
• Same code paths — both are Bitcoin, both use mempool API

What it requires

The TXO URI already encodes the chain — txo:btc:... can include network info. The deposit handler parses the chain, verifies against the right explorer, and credits the right balance type.

Extends to any UTXO chain

The same pattern works for testnet4 ↔ litecoin, testnet4 ↔ signet, or any pair of UTXO chains. The pod becomes a cross-chain exchange — no Ethereum, no wrapped tokens, no bridges. Just two UTXO chains, a pricing formula, and a Solid pod in the middle.

Depends on

• Multi-token support (Multi-token support per pod #192) for multi-pair pools
• Current single sat/token pair works without Multi-token support per pod #192